Final answer:
To solve inequalities, one must understand metric relationships and graphing techniques. Lines on a graph can be described as increasing or decreasing and their steepness. Linear equations take the form y = mx + b, representing a straight line on the graph.
Step-by-step explanation:
To solve inequalities accurately, it is essential to understand the relationship between metric measurements and how to graph these relationships. For instance, when defining the age of cars, if we say that the cars are at most a certain age, we can express this using an inequality symbol, ≤, which means 'less than or equal to'. To graph this inequality, one would draw a line corresponding to the maximum age and shade all the area representing ages up to and including that line. This shaded area indicates all possible ages of the cars that meet the condition.
When comparing two lines on a graph, we use the terms 'increasing' and 'decreasing' to describe their slopes. An increasing line goes upward as it moves from left to right, while a decreasing line goes downward. If line B is steeper than line A, it means that for every horizontal step taken, the vertical change in B is greater than in A.
For solving probability problems with inequalities, such as P(A AND B), we might use conditional formulas. For instance, if event A is the probability that x>12 and event B is the probability that x>8, we need to find the intersection of these two events to solve P(A AND B).
Turning to solving linear equations, we can see different forms, such as y = mx + b based on Practice Test 4 Solutions 12.1. These equations map out linear relationships where 'm' is the slope and 'b' is the y-intercept. For example, the equation y = 100(x) + 2,000 describes a linear relationship where the total payment y increases by 100 times the number of students x, with a starting payment of 2,000.